Abstract
It is known from the literature that a \(\varphi \)-function may be used to construct the \(\varphi \)-families of probability distributions. In this paper, we assume that one of the properties in the definition of \(\varphi \)-function is not satisfied and we analyze the behavior of the normalizing function near the boundary of its domain. As a consequence, we find a measurable function that does not belong to the Musielak–Orlicz class, but the normalizing function applied to this found function converges to a finite value near the boundary of its domain. We conclude showing that this change in the definition of \(\varphi \)-function affects the behavior of the normalizing function.
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Acknowledgement
The authors would like to thank CAPES and CNPq (Proc. 309055/2014-8) for partial funding of this research.
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de Andrade, L.H.F., Vigelis, R.F., Vieira, F.L.J., Cavalcante, C.C. (2017). Normalization and \(\varphi \)-function: Definition and Consequences. In: Nielsen, F., Barbaresco, F. (eds) Geometric Science of Information. GSI 2017. Lecture Notes in Computer Science(), vol 10589. Springer, Cham. https://doi.org/10.1007/978-3-319-68445-1_27
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DOI: https://doi.org/10.1007/978-3-319-68445-1_27
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